Problem 37 - General Chemistry

Question

You have two samples of different metals, metal \(\mathrm{A}\) and metal \(\mathrm{B}\), each having the same mass. You heat both metals to \(95^{\circ} \mathrm{C}\) and then place each one into separate beakers containing the same quantity of water at \(25^{\circ} \mathrm{C}\). a. You measure the temperatures of the water in the two beakers when each metal has cooled by \(10^{\circ} \mathrm{C}\) and find that the temperature of the water with metal \(\mathrm{A}\) is higher than the temperature of the water with metal \(\mathrm{B}\). Which metal has the greater specific heat? Explain. b. After waiting a period of time, the temperature of the water in each beaker rises to a maximum value. In which beaker does the water rise to the higher value, the one with metal \(\mathrm{A}\) or the one with metal \(\mathrm{B} ?\) Explain.

Step-by-Step Solution

Answer

Metal B has a greater specific heat. The water temperature in the beaker with metal A rises to a higher maximum value.

Step 1: Understand the Concept of Specific Heat

The specific heat capacity of a substance is defined as the amount of heat required to change the temperature of one gram of the substance by one degree Celsius. A higher specific heat means the material requires more energy to change its temperature by the same amount.

Step 2: Analyze the Initial Temperature Change

Both metals, A and B, cool down by 10°C when placed in water. However, since the water in the beaker with metal A reaches a higher temperature, it means that metal A transfers more heat energy to water in the initial phase of cooling.

Step 3: Determine Which Metal Has Greater Specific Heat

Since metal B results in a lower final temperature of water with the same mass cooling 10°C, it implies that metal B has absorbed more heat energy from the same amount of water. Thus, metal B has a greater specific heat capacity because it retains more energy while cooling down compared to metal A.

Step 4: Consider the Final Temperature Rise of Water

After some time, the temperature of the water in each beaker reaches a maximum. Since metal B has a higher specific heat and retains energy longer, it means it probably releases heat more slowly than metal A. Thus, metal A releases its heat more quickly, resulting in the water in the beaker with metal B staying cooler longer.

Step 5: Conclude Which Metal Results in Higher Maximum Water Temperature

Since metal A transfers more heat initially and quickly to the water, the maximum temperature of the water with metal A will be higher than that with metal B. This is because metal A has a lower specific heat and releases heat faster, raising the water temperature more than metal B does.

Key Concepts

Heat Transfer

Heat transfer is the process of heat moving from one body or substance to another. This movement typically occurs when two objects at different temperatures come into contact. Heat always moves from the hotter object to the cooler one until equilibrium is reached. For the exercise, both metals, when heated to 95°C, transfer heat to water, initially at 25°C. You might wonder why heat transfer is important. Well, it helps us understand how different materials react when subjected to heat.

• Metals, for instance, are often good conductors, meaning they can transfer heat efficiently.
• The key here is that each metal will transfer heat differently based on its properties.

In the problem, metal A and metal B, upon cooling by 10°C, transfer different amounts of heat to their respective beakers of water, explaining the temperature difference in the water's warmth.

Calorimetry

Calorimetry is the scientific method of measuring the heat involved in a chemical or physical process. By using a calorimeter, one can observe how heat is exchanged between substances. This is essential to determine the specific heat of materials accurately. In the given exercise, the change in water temperature is being observed to deduce information about the metals' heat capacities.

• Calorimeters help quantify heat released or absorbed, aiding in understanding the energy interplay between objects.
• This experiment doesn't use a complex calorimeter but follows the foundational principles of calorimetry.

When both metals are placed in water, the energy they release can subsequently be measured by the change in water temperature, revealing their specific heat capacities.

Temperature Change

The temperature change is the difference in temperature observed as substances heat up or cool down. It's crucial in understanding how heat transfer affects different materials. In the task, the metals initially cool by 10°C after being placed into water, causing the water to heat up. It's interesting how these changes give insight into the properties of the metals.
Observing temperature changes lets us conclude how much energy is lost or gained by a substance. The greater the temperature change, the more energy was transferred. However, a quick temperature change doesn't always indicate more energy transfer; rather, it can show that the substance has a lower specific heat capacity.
For instance, because water with metal A ends up warmer than with metal B initially, it suggests metal A has a lower specific heat capacity, meaning it transfers heat more easily, raising the water's temperature more significantly initially.

Metals and Their Properties

Metals are intriguing materials with a variety of thermal properties. They have different specific heat capacities which make them behave differently when heat is applied. These properties affect how they transfer heat and at what rates. In the exercise, metals A and B have unique heat interactions with water due to their specific heat differences.

• Metals with high specific heat absorb more heat before their temperature changes significantly.
• Conversely, metals with low specific heat increase in temperature more quickly for the same amount of heat.

This distinction is clarified in the problem scenario: Metal B, having a higher specific heat, absorbs more heat but warms the water less quickly; while metal A, lower in specific heat, releases heat more quickly, raising water's temperature faster initially. Understanding these characteristics helps explain why some metals are used for specific applications, like cookware or insulation.